Definition of adjoint in English:

adjective

He then went on to consider the case where the kernel is not symmetric and showed that in that case the eigenfunctions associated with a given eigenvalue occurred in adjoint pairs.

For the case of a finite-dimensional real linear space these are infinite systems whose adjoint cone is topologically closed.

Suffice it to say that adjoint functors pervade mathematics and this pervasiveness is certainly one of the most mysterious fact that category theory reveals about mathematics and probably thinking in general.